We provide introduction to graphs practice exercises, instructions, and a learning material that allows learners to study outside of the classroom. We focus on introduction to graphs skills mastery so, below you will get all questions that are also asking in the competition exam beside that classroom.

#### List of introduction to graphs Questions

Question No | Questions | Class |
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1 | Rectangle bars touching each other in which graph A. histogram B. bar c. pie D. line | 8 |

2 | Find the value of ( p ) if the points ( (2,1),(p,-1) ) and (-1,3) are collinear. | 8 |

3 | Write the ratio of the heights of highest peak and the lowest peak. A .22: 15 B . 15: 22 ( c, 20: 13 ) D. 13: 22 | 8 |

4 | The bar chart shows the number of workers employed by a trading companyin three years. Calculate the difference between the total number of male and female workers employed over those three years. ( mathbf{A} ) B. 2 ( c cdot 4 ) D. | 8 |

5 | Find the ratio of the total sales of laptop in Rajasthan state for both years to the total sales of laptop in Gujarat state for both years? Sales of laptop ( A cdot 8: 13 ) B. 13: 8 c. 11: 8 D. 8: 11 | 8 |

6 | With the help of which of the following will you describe the position of a pen on a table? A. Coordinate geometry c. Trignometry D. Proportions | 8 |

7 | Find the bar graph and state why? | 8 |

8 | Using graph paper, (take ( 2 mathrm{cm}=1 ) unit on both axis), plot ( boldsymbol{A}(-mathbf{4}, mathbf{2}) ) and ( boldsymbol{B}(mathbf{2}, mathbf{4}) ) ( A^{prime} ) is the image of ( A ) when reflected in the ( y ) -axis. Plot it on the graph paper and write the coordinates of ( A^{prime} . B^{prime} ) is the image of ( B ) when reflected about the line ( A A^{prime} . ) Join ( A-B-A^{prime}-B^{prime} ) and name the quadrilateral | 8 |

9 | Points (-3,-3),(4,-1),(6,6) and (-1,4) when joined in the given order form a A. parallelogram B. rectangle c. rhombus D. square | 8 |

10 | The graph above shows the number of units sold in 2015 for five different video games console. The price of consoles ( A, B, C, D, ) and ( E ) are ( $ 100, ) ( $ 150, $ 200, $ 250, ) and ( $ 300 ) respectively. Which of the five consoles generated the most total revenue? A . ( A ) в. ( B ) ( c . D ) ( D ) | 8 |

11 | Consider the following data gathered from a survey of a colony: Cricket ( begin{array}{ll}text { Favourate } & text { cricket } quad text { Basket } \ text { port: }end{array} ) sport: | 8 |

12 | Choose the correct answer from the alternatives given : Directions for questions 71 to 75: Study the following graph carefully to answer these questions. Production (in lakh tonnes) of six units | 8 |

13 | The performance of students in 1 st term and 2 nd term is as given below. Draw a double bar graph choosing appropriate scale and answer the following: Hindi Maths Subject: English ( 1^{s t} t e r m: ) 1 67 72 ( 2^{n d} ) term: 70 65 In which subject, has the children improved their performance the most? | 8 |

14 | The mid-points of the side of a triangle ( operatorname{are} D(6,1), E(3,5) ) and ( F(-1,-2) ) then the vertex opposite to D is A. (-4,2) в. (-4,5) c. (2,5) (年. (2,5) D. (10,8) | 8 |

15 | In which graph, frequency is represented by the area of each rectangle? A. bar B. pie c. line D. histogram | 8 |

16 | If ( A ) and ( B ) are two points having coordinates (3,4) and (5,-2) respectively and ( P ) is a point such that ( P A=P B ) and area of ( P A B=10 ) sq. units, then coordinates of ( mathrm{P} ) are в. (7,2)( &(1,0) ) c. (2,7)( &(4,13) ) D. (7,4)( &(13,4) ) | 8 |

17 | If the line ( 3 x-4 y=lambda ) cuts the circle ( x^{2}+y^{2}-4 x-8 y-5=0 ) in two points then limits of ( lambda ) are A . [-35,15] В . (-35,15) c. (-35,10) D. (-35,15] | 8 |

18 | The following table shows the interest paid by a company (in lakhs): ( begin{array}{lll}text { 1995- } & text { 1996- } & text { 1997- }end{array} ) Year Interest in lakhs [ 20 ] 25 of rupees) Draw the bar graph to represent the above information. | 8 |

19 | Find the coordinates of the point on the X-axis which is at distant 5 units from ( A(4,4) ) | 8 |

20 | Co-ordinate of point P on a number line is 7. Find the coordinate of point on the Number line which is at a distance of 8 units right to point ( P ) | 8 |

21 | Choose the correct answer from the alternatives given : Directions for questions 71 to 75: Study the following graph carefully to answer these questions. Production (in lakh tonnes) of six units of a company in 2006 and 2007 What is the average production of all | 8 |

22 | A graph showing two sets of data simultaneously is known as A. pictograph B. histogram c. pie chart D. double bar graph | 8 |

23 | Let ( (x+y, 1) ) and ( (3, x-y) ) be equal ordered pairs then find the value of ( x, y ) | 8 |

24 | Answer the Following: Explain the techniques of drawing a Histogram. | 8 |

25 | Total sales of branches ( B_{1}, B_{3}, ) and ( B_{5} ) together for both the years (in thousand numbers) is: ( A cdot 250 ) 3. 310 ( c .435 ) 0.560 | 8 |

26 | The equation of line perpendicular to ( boldsymbol{x}=boldsymbol{c} ) is ( mathbf{A} cdot y=d ) B. ( x=d ) c. ( x=0 ) D. None of these | 8 |

27 | Give Reasons A histogram is not a diagram. | 8 |

28 | Total sales of branch ( B_{6} ) for both the years is what percent of the total sales of branch ( B_{3} ) for both the years? A. ( 68.54 % ) в. ( 71.11 % ) ( c .73 .17 % ) D. ( 75.55 % ) | 8 |

29 | Which city has more people reading newspaper than watching T.V? When reading newspaper people watching TV A. Patna B. Kolkata C. Mumbai D. Delhi | 8 |

30 | The point ( left(x_{1}, y_{1}right),left(x_{2}, y_{2}right),left(x_{1}, y_{2}right) ) and ( left(x_{2}, y_{1}right) ) are always ( ? ) A. Collinear B. concyclic c. vertices of square D. vertices of a rhombus | 8 |

31 | Name the axis on which following point lie (-5,-8) | 8 |

32 | Draw a triangle whose side are represented by ( boldsymbol{x}=mathbf{0}, boldsymbol{y}=mathbf{0} ) and ( boldsymbol{x}+ ) ( boldsymbol{y}=mathbf{3} ) in the Cartesian system Also find the coordinates of its vertices. | 8 |

33 | Give Reasons A frequency polygon can be drawn with the help of a Histogram. | 8 |

34 | What is the average sale of all the branches (in thousand numbers) for the year ( 2006 ? ) ( A cdot 73 ) ( B .80 ) ( c cdot 83 ) 0.88 | 8 |

35 | Fill in the blanks with suitable word: The ( x ) -coordinate is called as | 8 |

36 | What is the ratio of the total sales of branch ( B_{2} ) for both years to the total sales of branch ( B_{4} ) for both years? ( A .2: 3 ) ( B .3: 5 ) ( mathbf{C} cdot 4: 5 ) D. 7: 9 | 8 |

37 | In which city number of people watching T.V is same as people reading newspaper? ( mathbb{Z} ) people reading newspaper ( A ). Delhi B. Mumbai C. Kolkata D. Patna | 8 |

38 | In a statistical diagrammatic representation, rectangular bars drawn after a discontinuous series is called graph. A. bar B. histogram c. pie D. frequency curve | 8 |

39 | Consider a square of side length 1 unit. What is its area? | 8 |

40 | The following pie chat gives the marks second in an examination by a student in Hindi, English, Mathematics, Social Science and Science. If the total marks obtained by the student were 540 answer the following questions. All values are shown in degrees. Examine whether the sum of the marks obtained in Social Science and Mathematics is more than that in Science and Hindi. | 8 |

41 | During the period ( 2007-2010 ), the minimum rate of increase in sales is in the case of? A. Dove 3. Himalayas c. Detto D. Lux | 8 |

42 | Which is a two dimensional graph? ( A cdot ) pie B. bar c. histogram D. frequency curve | 8 |

43 | The diagram is drawn on a square grid Of the triangles marked ( P, Q, R ) and ( S ) which is the image of triangle ( X ) under a reflection in the line ( M N ? ) ( A ) 3. ( Q ) ( c . R ) ( D ) | 8 |

44 | Write the length of the perpendicular drawn from the point ( P(3,5,12) ) on ( x ) axis. | 8 |

45 | In a triangle ( A B C, ) the co-ordinates of vertices ( A, B ) and ( C ) are (4,7),(-2,3) and (0,1) respectively. find the equation of median through vertex ( boldsymbol{A} ) Also, find the equation of the line through vertex ( B ) and parallel to ( A C ) | 8 |

46 | Study the graph carefully and answer the question: The number of people who prefer playing Tennis in 2006 is how many millions less than the number of people who prefer playing Tennis in ( 2005 ? ) A . 110 B . 105 ( c .100 ) D. 95 | 8 |

47 | When proving that a triangle is a right triangle using coordinate geometry methods you must A. show that the slopes of two of the sides are negative reciprocals creating perpendicular lines and right angles B. show that the lengths of the sides satisfy the Pythagorean Theorem thus creating a right angle C. both choices 1 and 2 may be used D. neither choice 1 nor 2 may be used E. none of these | 8 |

48 | Given below are some points, with thei ( boldsymbol{P}(mathbf{4}, mathbf{3}), boldsymbol{Q}(-mathbf{3}, mathbf{2}), boldsymbol{R}(mathbf{5}, mathbf{1}), boldsymbol{S}(mathbf{0},-mathbf{4}) ) What is the ( x- ) coordinate of point ( P ) ( ? ) | 8 |

49 | How many dimension does a surface has ? | 8 |

50 | Plot the points (0,0)(0,3)(3,4)(4,0) in graph sheet. Join the points with straight lines to make a rectangle. Find the area of the rectangle. | 8 |

51 | The number of students spent more than 5 hours in watching ( mathrm{TV}, ) is A . 32 B. ( c ) D. 14 | 8 |

52 | Which of the following statements is false? A. The x-coordinates of all points to the right of the y-axis are positive B. The y- coordinates of all points above the x-axis are positive C. The ( y ) – coordinates of all points below the x-axis are positive D. The x-coordinates of all points to the left of the y-axis are negative | 8 |

53 | If Set B has 200,000 elements, calculate the difference between number of negative and even numbers of set B. Negative and Even Number Distributions | 8 |

54 | The sales have increase by nearly ( 99.9 % ) from 2007 to 2010 in the case of? A. Rexona 3. Dettol ( c cdot operatorname{Lux} ) ( D . ) Dove | 8 |

55 | Fill in the blank: The system used for describing the position of a is called Cartesian system. A. Point B. Circle c. Line D. Square | 8 |

56 | For which of these would you use a histogram to show the data. The number of letters for different areas in a postman’s bag. | 8 |

57 | Of the following, which best approximates the percent decrease in consumption of wood power in the United States from 2000 to ( 2010 ? ) Renewable Energy Consumption ( A ) B. 11 ( c .21 ) ( D cdot 26 ) | 8 |

58 | Reflect shape ( A ) in ( x-a x ) is. Label the image shape B | 8 |

59 | If ( M N ) is a straight line on a cartesian plane. The co-ordinates of ( mathrm{N} ) are (12,13) and ( M N=9 ) units. Find the co- ordinates of ( mathrm{M} ) A ( .(21,13) ) B. (12,22) c. (12,4) D. (3,13) | 8 |

60 | Position of an object in plane can be easily find out by the help of: B. Trignometry c. coordinate geometry D. Proportions | 8 |

61 | A graph drawn using vertical bars is called A. Bar graph B. Line graph c. Pictograph D. Pie graph | 8 |

62 | Find what the following equations become when the origin is shifted to the point (1,1)( ? ) (i) ( x^{2}+x y-3 x-y+2=0 ) ( boldsymbol{x}^{2}-boldsymbol{y}^{2}-boldsymbol{2} boldsymbol{x}+boldsymbol{2} boldsymbol{y}=mathbf{0} ) (iii) ( boldsymbol{x y}-boldsymbol{x}-boldsymbol{y}+mathbf{1}=mathbf{0} ) ( boldsymbol{x} boldsymbol{y}-boldsymbol{y}^{2}-boldsymbol{x}+boldsymbol{y}=mathbf{0} ) | 8 |

63 | What is the percentage of the total sales of laptop in the state of Haryana and Rajasthan for both the years? Sales of laptop A . ( 23.13 % ) B . ( 26.54 % ) c. ( 27.4 % ) D. ( 31.34 % ) | 8 |

64 | The graph shows the number of basketball titles won by the boys team and the girls team for three different school teams. Based on the data in the graph, which of the following statements is true? A. The ( F . P . S ) teams together have won the greatest total number of basketball titles B. The girls L.P.S team has won exactly twice as many titles as the ( G . P . S ) boys and girls teamsm together C. The girls ( F . P . S ) team has won more titles than the girls ( L . P . S ) team D. The ( L . P . S ) teams together have won the greatest total number of basketball titles | 8 |

65 | The sales of Dove in 2010 was by what percent less than the sales of Dove in ( 2007 ? ) A. ( 40 % ) 3. ( 60 % ) ( c .70 % ) ( 0.50 % ) | 8 |

66 | Find the average sales of laptop of all the states for the year 2004 ( A, 9,7 ) 3. 11.71 ( c .14 .45 ) D. 15.23 | 8 |

67 | The point X-axis which is equidistant from the point (3,5) and (4,2) is A. (-6,0) B . (-7, 0) c. (7, 0) D. (-5, 0) | 8 |

68 | Figure is a graph of which of the following? A ( cdot x^{2}+y^{2}=9 ) в. ( |x|=3 ) and ( |y|=3 ) c. ( |x+y|=3 ) D. ( |x|+|y|=3 ) E . ( x-y=3 ) | 8 |

69 | In which graph, rectangle bars are separated? A . line B. pie ( c . ) bar D. histogram | 8 |

70 | The following histogram shows the frequency distribution of the ages of 22 teachers in a school: What is the number of eldest and youngest teachers in the school? | 8 |

71 | Write the name of the point where the two axes meet. | 8 |

72 | What is the ratio of the number of people who prefer playing Cricket in 2001 to the number of people who prefer playing Tennis in the year ( 2003 ? ) A . 14: 17 B . 16: 13 c. 15: 11 D. 13: 15 | 8 |

73 | Which is the highest peak? ( A cdot A ) B. E ( c cdot c ) ( D cdot B ) | 8 |

74 | Which of the points ( A, B, C ) and ( D ) below has the coordinates of the origin? ( A cdot A(-3,1) ) B. B(0, 0) c. ( c(1,2) ) D. D(9, o) | 8 |

75 | Give Reason: A histogram is a two dimensional ( operatorname{graph} ) | 8 |

76 | The diagram below shows part of the ( operatorname{graph} ) of ( y=frac{b-x}{c x+d} ) The ( x ) intercept is (6,0) The vertical asymptote is ( boldsymbol{x}=-3 ) The horizontal asymptote is ( y=-1 ) Find the value of ( boldsymbol{d} ) | 8 |

77 | Select and write the most appropriate answer from the given alternatives for question: The cartesian equation of the line passing through the points ( boldsymbol{A}(mathbf{4}, mathbf{2}, mathbf{1}) ) and ( boldsymbol{B}(mathbf{2},-mathbf{1}, mathbf{3}) ) is A. ( frac{x+4}{2}=frac{y-2}{3}=frac{z-1}{-2} ) в. ( frac{x-4}{-2}=frac{y-2}{-3}=frac{z-1}{-2} ) c. ( frac{x-4}{2}=frac{y-2}{3}=frac{z-1}{-2} ) D. ( frac{x-4}{-2}=frac{y-2}{3}=frac{z-1}{-2} ) | 8 |

78 | Given ( A ) -B-C the co-ordinate of point ( A ) is the smallest.lf ( mathrm{d}(mathrm{A}, mathrm{B})=7.5, mathrm{d}(mathrm{B}, mathrm{C}):=13,8 ) and the coordinate of point ( mathrm{B} ) is ( 8.5, ) then find the coordinates of points ( A ) and ( C ) ( A cdot A leftrightarrow 0, C leftrightarrow 63.2 ) B. ( A leftrightarrow 5, C leftrightarrow 40 ) ( mathrm{c} cdot mathrm{A} leftrightarrow 1, mathrm{C} leftrightarrow 22.3 ) D. ( A leftrightarrow 3, C leftrightarrow 18 ) | 8 |

79 | The sales of Lux in 2010 was by what percent more than the sales of Rexona in 2007? A. ( 60 % ) 3. ( 50 % ) ( c .80 % ) ( 0.90 % ) | 8 |

80 | What percent to the average sales of branches ( B_{1} B_{2} ) and ( B_{3} ) in 2007 is the average sales of branches ( B_{1}, B_{2}, ) and ( B_{6} ) in ( 2006 ? ) ( A .75 % ) В. ( 77 % ) ( c .87 .5 % ) D. ( 70 % ) | 8 |

81 | What are the different types of graphs? | 8 |

82 | Give Reason: A histogram is not a diagram. | 8 |

83 | If the line ( 2 x+5 y=k ) passes through origin then ( k= ) ( mathbf{A} cdot mathbf{0} ) B. c. -1 D. | 8 |

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